Left-hander Moeen, who began his career at Edgbaston before opting for a move to Worcestershire six years ago, gorged himself against a depleted Bears attack by rattling up his seventh one-day century from just 75 balls.
Moeen's innings laid the foundations for Worcestershire's imposing 291 for nine which proved too much for Warwickshire, who were undermined by paceman Graeme Cessford, an RAF corporal who has been given a sabbatical from active service to pursue a career in county cricket, whose one day-best figures of four for 24 included an opening burst of three for two in 18 balls.
Warwickshire's defeat leaves them in danger of finishing bottom of the group but this competition is low on their list of priorities, as their decision to rest front-line players including Keith Barker, Rikki Clarke, Tim Ambrose and Ian Westwood ahead of tomorrow's LV= County Championship match against Somerset demonstrated.
Only off-spinner Jeetan Patel, who returned a season's-best four for 43, managed to check Worcestershire's progress, but by then Moeen and captain Daryl Mitchell had given them their best start to an innings this season with an opening stand of 104 in 14 overs.
Moeen was initially overshadowed by Mitchell, who passed 50 for the sixth time in the competition this season before he was bowled for a quickfire 60 shaping to cut a full length ball from Darren Maddy.
But Moeen then accelerated superbly, moving from a 42-ball half-century to three figures in only 33 more deliveries with nine fours and three sixes. Moeen added three more fours in 10 balls before he was stumped advancing down the pitch to Patel.
Alexei Kervezee was content to play a supporting role in a second wicket partnership of 113 with Moeen, but he played himself back into a semblance of form with only his third half-century in all cricket in a lean season.
Patel's accuracy and three wickets in four balls from Steffan Piolet in an eventful final over kept Worcestershire below 300, but Warwickshire buckled against Cessford's pace.
Moeen then contributed with the ball by snaring Scotland international Freddie Coleman and Patel with his off-spin to catches in the deep.
Mitchell throttled the innings by taking three wickets and Warwickshire only managed to avoid their record margin of runs defeat in 40 overs cricket - 146 against Gloucestershire in 1973 - thanks to a battling unbeaten 47 from Laurie Evans as they drifted to 151 all out.